Quantum Naughts and Crosses 13

(continued from here)

This is the yz-plane with x = +1. It is the face of the mandalic cube that would be presented were the cube rotated 90 degrees clockwise.(1) Its resident tetragrams are formed from lines 2, 3, 5 and 6. Lines 1 and 4 are not included in the resident tetragrams because the x-dimension value is unchanging (+1) throughout this face of the mandalic cube. The z-axis (lines 3 and 6) is presented horizontally here, positive toward the viewer’s left. The y-axis (lines 2 and 5) is presented vertically, positive toward the top. The corresponding Cartesian triples are shown directly beneath the hexagram(s) they relate to.

The complementary(2) face of the mandalic cube, the yz-plane with x = -1, can be generated by changing lines 1 and 4 in every hexagram above from yang(+1) to yin(-1). Were we to do that and also view the resulting plane from a vantage point inside the cube we would then see a patterning of resident tetragrams identical to that in the plane above. The only difference apparent would be the substitution of yin lines for yang lines at positions 1 and 4.

We might have justifiably started out here by viewing the yz-plane with x = -1 from without the cube and followed with viewing the yz-plane with x = +1 from inside the cube had the die not already been cast. The problem with that attack given the present circumstances is that we have previously begun our consideration of the members of the the other two face pairs with the positive member from outside the cube. By preserving that consistency we end up with a jigsaw puzzle the parts of which can readily be fitted together to recreate the whole. Any inconsistency at this point can only result in failure.(3)

(1) This assumes that we begin with the reference face we have been using (xy-plane, z = +1) toward the observer seated at the bridge table.

(2) Mandalic geometry views opposite faces of the mandalic cube as being complementary rather than antagonistic or adversarial. This seems almost unnecessary to point out when the six planes that constitute the Cartesian cube are viewed as a single complex whole. There is a synergy of action simultaneously involving all component parts of the whole and there is an even greater degree of complex interactivity involving the component parts of the higher dimension mandalic cube.

The parts may indeed at times be in conflict or opposition with one another but at other times work together to create an effect. For a possible analogy think here of the constructive and destructive interference in which two or more wave fronts may participate. The I Ching, although it does not explicitly view the hexagrams and their component trigrams and tetragrams in the context of a geometric cube, nonetheless attributes these alternative and alternating reciprocal capacities to yin and yang and to all the line figures formed from them.

(3) This is much more than a simple matter of human convention. In this case we really are dealing with actual laws of nature, however cryptic and concealed they might be. This is not the right time to elaborate fully on what is involved here. Suffice it for now to point out that the approach we have chosen allows the three Cartesian and six additional mandalic dimensions to conform together with one another to certain combinatorial principles that nature demands they do.

For example, the three faces of the cube in which the hexagram consisting of six yang lines is found must fit together at a single point which forms one of the eight vertices of the cube by superimposing the three occurrences of this hexagram in the three different Cartesian planes at that single point. A similar requirement exists for all the other vertices of the cube as well. When all these various requirements are met all six faces can fit together snugly to form the cube. Were even just one of the requirements not satisfied the cube as a structural and functional whole would be unable to form.

We are talking here not simply about geometric shapes but about energetic physical phenomena as well. Ultimately this is not just a matter of composing a cube but of confronting the reality that dimensions fit together and force fields interact only in specific predetermined ways which we have no power to change. Moreover, this is just one indication that mandalic geometry describes more than literal locations existing in a topological space. It also corresponds in some sense to a state space, an abstract space in which different “positions” represent states of some physical system.

© 2014 Martin Hauser